Members of two Libyan tribes -- who fought together to unseat Moammar Gadhafi and his loyalists -- clashed Saturday, infighting among opposition forces that comes as a key ally of the longtime leader vowed to keep up the fight.

Ahmed Hussein, a resident of Badr, told CNN that Berber tribesmen from Nalut used Kalashnikov rifles and machine guns in an attack on Seaan Arab forces in that mountainous western Libyan city. A family of three caught in the crossfire was killed, he claimed.

"Nalut rebels were welcome to our town during the revolution, but now they barge in with their weapons searching the houses and scaring the residents," said Hussein, who witnessed the attacks.

Seaan Arab fighters, meanwhile, attacked Berbers from Nalut while they were posted in the Kremia neighborhood of Tripoli.

Louie Zintan, a Libyan resident who witnessed this clash and works for CNN, said he heard the two sets of anti-Gadhafi forces negotiating a truce and talking of exchanging prisoners. A Tripoli-based anti-Gadhafi fighter serving as a mediator warned that they might ignite a tribal war, should the fighting continue.

A National Transitional Council spokesman confirmed the confrontations, saying it was the second time the Amazigh -- another term for the Berber group that comprises about 10% of Libya's population and is not of Arab descent, according to Amazigh student and opposition fighter Ahmed Hatem -- had clashed with the Seaan Arab forces.

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It is the first time, however, that a firefight has occurred outside mountain areas and instead in Tripoli, said NTC spokesman Abdul Rahmad Busin.

"It is just an isolated incident, due to old feuds spilling into the streets," Busin said, adding he was hoping for a positive resolution to such issues. "The (opposition) security council is working really hard to unite all the brigades."

Just over a month ago, tribesmen around Libya celebrated as anti-Gadhafi forces captured the capital of Tripoli, after having taken most other major cities in the North African nation. Since then, many nations have recognized the transitional council -- including past allies of Gadhafi and the African Union -- as the legitimate leaders of Libya's government.

But Gadhafi loyalists are still offering stiff resistance in Bani Walid, Sabha and Sirte, and Moammar Gadhafi himself remains at large.

Musa Ibrahim, a spokesman for the longtime Libyan ruler, vowed again Saturday that loyalists will not give up.

"We are not scared of fighting," Ibrahim, who had been a major public face representing Gadhafi, said in a phone interview with Rai TV, a pro-Gadhafi station based in Syria. "We will fight until martyrdom."

Ibrahim effectively claimed victory in Bani Walid, one of the few Libyan municipalities not yet under opposition control.

"Bani Walid is cleansed and the bodies of the NATO gangs are thrown in (the nearby) valleys and mountains," he said.

In Sirte, Ibrahim claimed that he was part of a 24-person contingent involved in a fight that ran over a day and a half.

The Gadhafi spokesman discounted rumors that he himself had been captured. Another NTC spokesman, Adel Ghulaek, earlier described the rumor of Ibrahim's capture as a "trick spread by the Gadhafi loyalists."

The transitional council said this week that Sirte was surrounded by revolutionary forces and that it believed about 5,000 pro-Gadhafi fighters were in the city.

In a press conference Saturday, the group's chairman Mustafa Abdul Jalil said civilians there had 48 hours to leave.

Hussein al-Teer, a transitional council field commander situated near the central coastal city, said anti-Gadhafi military leaders meeting Saturday night agreed to give residents of the besieged city more time to leave before launching a full-scale assault.

"We will conduct the major offensive on Sirte after we make sure that most of the families have already left the city," al-Teer said late Saturday. "This will probably take a few days."

Thousands of civilians have fled Sirte, still a stronghold of Gadhafi loyalists, as fighting has intensified there in recent weeks.

But on Saturday the number of families seen leaving the city -- which is Moammar Gadhafi's birthplace -- dropped dramatically after a route they were using was shelled.

At least three family members were killed, including a child, when a mortar round fired by pro-Gadhafi forces landed on a long line of civilian vehicles that were trying to flee the city, local commander Mohammed Ibraheem said.

Transitional council fighters told CNN this was an attempt by Gadhafi's forces to stop families leaving Sirte so they can use them as human shields and stop anti-Gadhafi fighters from attacking.

"Sirte families have to find another road to flee Sirte because clearly Gadhafi's forces found out about this road and attacked it," Ibraheem told CNN.

He said at least 100 families had been using the road to escape every day before Saturday's attack.

A CNN team at the scene Saturday morning witnessed a few families who managed to leave the city by a different road -- but only families living on the southern outskirts of Sirte, rather than the center of the city, could manage it.

Many others have already escaped what aid agencies say are dire conditions.

"There are around 10,000 people who have fled the city, and are displaced in the area between Sirte and Harawa," said Souad Masoudi, a spokeswoman for the International Committee of the Red Cross.

"With the assistance of the Libyan Red Crescent, we have been able to assess their needs, set them up in tents and have successfully distributed kits containing food, baby milk, water, diapers and cooking material to sustain them, especially (if) they do not have running water."

The spokeswoman said her organization would continue its efforts to deliver much-needed medical supplies into Sirte.

Red Cross workers had previously tried to enter the city by boat but "had to turn back due to the security situation."

They will now try to enter after speaking with people on both sides of the conflict and doctors in the city, Masoudi said. They hope to deliver medical supplies to the hospitals and kits to treat the war wounds of up to 400 patients, she added.

A testy exchange erupted between Sen. John McCain and Joint Chiefs Chairman Gen. Martin Dempsey during the latter's testimony about September's deadly attack on the U.S. diplomatic mission in Benghazi, Libya.